I still get quest xp and level up appropriately, but I can't see the actual xp bar to the right of my level number. My mouse recognizes the space where the bar should be, and if I click on it, it sends me to the quest page. I just can't see it.
Even if you didn't have a card associated with PSN, it's a good idea to change your passwords and contact, say, Experian, to put a 90-day fraud alert on your identity. All the details that they got about address and birthday are the kind of details that one would need if one were thieving identities.